Reigning champion Kim Clijsters insisted her game was still a work in progress despite easing into the third round of the US Open with a 6-2 6-1 victory over Australian Sally Peers.

Clijsters has lost just eight games so far at Flushing Meadows but admitted there was plenty of room for improvement after dropping her serve twice against qualifier Peers.

The 27-year-old Belgian, who won the title 12 months ago in only her 14th match and third tournament since coming out of retirement, also managed to get just 51% of her first serves in and committed 21 unforced errors.

"I just had to find my footing again a little bit," said Clijsters, who is seeded second this year behind Denmark's Caroline Wozniacki, the player she beat in last year's final.

"I felt as the match went on I got to read her game a bit better and moved a bit better, but I still have a little further to go before I play my best tennis."

Earlier on the third day Serbia's Ana Ivanovic revealed she feels close to rediscovering the form which made her world number one after also cruising into the third round.

Ivanovic dropped just five games in beating Ekaterina Makarova in the opening round and lost just three today as she thrashed China's 21st seed Jie Zheng 6-3 6-0.

The 22-year-old, who has dropped to 40th in the world rankings due to injuries and a loss of form, had lost two of her previous three matches against Zheng, including at Wimbledon in 2008 when Zheng was ranked 133rd and Ivanovic number one.

"I remember a couple of years ago when I was here and I was saying, even though I'm number one I don't feel I'm playing as number one," Ivanovic said.

"But now I feel like I'm playing like a top-10 player, I have confidence that I can beat these players. That's huge for me."

Third seed Venus Williams was pushed all the way by Canadian qualifier Rebecca Marino, the two-time champion eventually recording a 7-6 (7/3) 6-3 victory.

Williams will face another qualifier in the third round after Mandy Minella, the world number 185 from Luxembourg, dispatched 32nd seed Tsvetana Pironkova for the loss of just four games.

"It was challenging, not just with the conditions, but also my opponent. She served so well and mixes up her shots," Williams said. "It seemed like every time I had an opening she came up with a big serve, so I guess I know what it's like now playing myself."

Elsewhere, French Open champion Francesca Schiavone, the sixth seed, hammered Maria Elena Camerin 6-2 6-1, while 24th seed Daniela Hantuchova came from a set down to beat American Vania King 5-7 6-3 6-4.

Number 12 seed Elena Dementieva had an easier time in seeing off Austria's Sybille Bammer 6-3 6-4, while 20th seed Anastasia Pavlyuchenkova also advanced to the third round with a 6-2 6-4 win over India's Sania Mirza.

But former Wimbledon finalist Marion Bartoli, the 13th seed, lost in straight sets to fellow Frenchwoman Virginie Razzano, who will play Ivanovic in the third round.

Fifth seed Samantha Stosur, runner-up in the French Open this year, also advanced with a 6-1 6-4 victory over fellow Australian Anastasia Rodionova.